Correct size and working Cat can't effect power, simply not possible, clogged Cat can, just like a clogged straight pipe can.
Stock exhaust systems take advantage of what was learned in racing engines, one of these things is "scavenging" exhaust systems.
When several cylinders will be hooked to one exhaust pipe you can create a LOW pressure at the exhaust valves using the Velocity of the exhaust.
The calculations for this is above my pay grade, I just know it works, lol.
The diameter of the exhaust pipes at the head and the length of that pipe and then the diameter of the Collector pipe(where that banks exhaust pipes connect) all determine when the LOWEST pressure will occur in the RPM band.
Most stock exhaust systems are set for mid-RPM range.
Most 3rd party headers are set up for low-RPM range
Racing headers are setup for high-RPM Range
You don't get more power, it just changes when the extra scavenged power will be available.
Scavenged power is from the crank using less power to push out exhaust, the lower pressure pulls it out, so crank has more power for the rear wheels.
From the collector back needs to be the same size or larger pipe, but there are also newer "H" or "X" exhaust system used on V engines with dual exhaust, basically a crossover pipe or pipes that add an extra scavenging ability because of the opposite exhaust pulses that exist on each bank.
The "Myth" of back pressure comes from factory(stock) scavenging exhaust systems.
People would determine that a "free flowing" exhaust would have to be better than a stock exhaust system.
So they would install larger pipes from the heads back.
Then on a test drive they found they LOST power, "WTF!!!"
So they would, incorrectly, think "this engine must need back pressure", opps, lol.
The larger pipes reduced the Velocity at the collector so there was little or no pressure drop at the exhaust valves, they lost the scavenged power with the "free flowing" exhaust, so their results were to be expected but their conclusion was incorrect
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